# Signal Characteristics

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1 Signal Characerisics Analog Signals Analog signals are always coninuous (here are no ime gaps). The signal is of infinie resoluion. Discree Time Signals SignalCharacerisics.docx 8/28/08 10:41 AM Page 1

2 Discree Time Signals: Informaion abou he signal magniude is available only a discree poins in ime r Discree daa Sampling: The process of obaining discreized informaion from a coninuous variable a finie ime inervals. SignalCharacerisics.docx 8/28/08 10:41 AM Page 2

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7 y() y() y() Characerizaion of Signals A - Deerminisic B Random (sochasic) 1. Saic Dynamic a. Simple periodic waveform b. Complex periodic waveform SignalCharacerisics.docx 8/28/08 10:41 AM Page 7

8 y() y() y() A Deerminisic (con) 2. Dynamic (con) c. Aperiodic waveform Sep Ramp Pulse SignalCharacerisics.docx 8/28/08 10:41 AM Page 8

9 B Random (sochasic) Characerizaion of Signals 1 () y SignalCharacerisics.docx 8/28/08 10:41 AM Page 9

10 Signal Characerisics: Definiions Magniude - generally refers o he maximum value of a signal Range - difference beween maximum and minimum values of a signal Ampliude - indicaive of signal flucuaions relaive o he mean Frequency - describes he ime variaion of a signal Dynamic - signal is ime varying Saic - signal does no change over he ime period of ineres Deerminisic - signal can be described by an equaion (oher han a Fourier series or inegral approximaion) Non-deerminisic - describes a signal which has no discernible paern of repeiion and canno be described by a simple equaion. Mean - average or saic porion of a signal over he ime of ineres. Someimes call he dc componen or he dc offse of he signal [Excel ip: Mean = AVERAGE(numbers...)] RMS - roo-mean-square - average value of he square of he signal over he ime of ineres. [Excel ip: RMS = SQRT(SUMSQ(numbers 1 o n )/n)] SignalCharacerisics.docx 8/28/08 10:41 AM Page 10

11 Signal Analysis Average or Mean Value Provides a measure of he saic porion of a signal over a period of ime. y 1 2 y() d 1 2 d This is ofen referred o as he dc componen or dc offse. Flucuaing or AC Componen The dynamic porion of a signal, y, is characerized by he various measures of he magniude and he amoun of flucuaion. One such characerizaion is he rms value, or roo mean square. The flucuaing porion alone is ofen characerized by he a erm called he variance, 2, or he square roo of he variance he sandard deviaion,. Where, y', is he rue mean value of he signal. SignalCharacerisics.docx 8/28/08 10:41 AM Page 11

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13 Digial Sampling Quanizaion: The runcaion of an analog signal o a finie resoluion. A/D Resoluion: is defined as he smalles volage incremen ha will cause he digial oupu o change (a change in he leas significan bi of he ADC oupu value) A/D Resoluion is a funcion of he ADC digial oupu word size and he analog inpu volage range. The inpu volage range, E FSR, is divided ino 2 M equal incremens where M is he number of bis in he ADC oupu word. Q = E FSR / 2 M Lab ADC: 12 bi digial oupu word size 20 Vol analog inpu range Variable inpu signal gain Gain: an signal amplificaion facor. If an inpu signal is amplified by a facor he effecive E FSR is changed. Q = E FSR /Gain/ 2 M Lab ADC: Q = 20V /Gain/ 2 12 SignalCharacerisics.docx 8/28/08 10:41 AM Page 13

14 Lab ADC Gain Values: 1, 2, 5, 10, 100 & 200 Lab ADC Example, gain=200: Q = 20V/200/4096 = V Example: E FSR = 4 V, M = 2, Q = 4/2 2 = 1V SignalCharacerisics.docx 8/28/08 10:41 AM Page 14

15 Quanizaion Error Error = (ADC Oupu - True Value)/True Value Example: From figure 7.7 if he inpu value is 1.5 wha is he percen error? Error = (1-1.5)/1.5 = -1/3 V or -33% Error can range from 0 o 1 vol or he e Q = Q Inpu volage shifing is used o minimize he error by adding a bias of Q/2. Think of his as a change from runcaion o rounding off. The error hen becomes e Q = ±½Q ADC Signal-o-noise raio: (SNR) relaes he power of he signal (Ohm's Law E 2 /R) o he power of he smalles signal change, Q, ha can be deeced E 2 /R2 M The recording indusry expresses he ADC SNR in decibels (db): SNR[dB] = 20 log 2 M SignalCharacerisics.docx 8/28/08 10:41 AM Page 15

16 Aliasing How rapidly do we need o sample a signal in order o accuraely describe i? The answer depends on he frequency conen of he signal. SignalCharacerisics.docx 8/28/08 10:41 AM Page 16

17 The sampling heorem provides he guideline. The sample rae mus be high enough o sample a leas wo poins per period of he highes frequency (sine wave) conained in he measured signal. SignalCharacerisics.docx 8/28/08 10:41 AM Page 17

18 If he sampling rae is oo low, aliasing will occur. Tha is, signals will be disored (Fig b,c) and may appear o have frequencies lower han heir acual value, as shown by Figure 6.32d 1, 7.2 2,3. Noice ha in he figure above i is impossible o disinguish beween he wo waveforms by sampling a he poins shown. As shown on p , 273 2,3 he maximum frequency componen which can be accuraely measured is he Nyquis frequency: f N f s = = 1 2,3 (6.63, 7.8 ) where δ is he sampling inerval. The A/D converers in he lab have a maximum sampling rae of approximaely 100,000 Hz wih he sofware we are using. Thus we can reproduce signals wih frequencies o abou 50,000 Hz. The converers have a resoluion of 12 bis, so he quanizaion error is 1 par in 2 12 or 1 par in 4096 of full scale. We will alk laer abou he elecronic circuis which are used. SignalCharacerisics.docx 8/28/08 10:41 AM Page 18

19 Figure 7.3 The folding diagram for alias frequencies. SignalCharacerisics.docx 8/28/08 10:41 AM Page 19

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